In March, Victoria and David had beads in the ratio 13 : 9. In April, each of them gave away the same number of beads. Victoria then had twice as many beads as David.

1. Find the ratio of the number of beads David had in March to the number of beads he had in April.
2. Find the ratio of the total number of beads both had in March to the total number of beads both had in April.

	Victoria	David	Difference
Before	13x1 = 13 u	9x1 = 9 u	4x1 = 4 u
Change	- 5 u	- 5 u
After	2x4 = 8 u	1x4 = 4 u	1x4 = 4 u

(a)
Since Victoria and David gave away the same number of beads, the difference in the number of beads between Victoria and David at first and in the end remains the same.

Make the difference in the number of beads at first and in the end the same. LCM of 4 and 1 is 4.

David's beads in March : David's beads in April
9 : 4

(b)
Total number of beads in March
= 13 u + 9 u
= 22 u

Total number of beads in April
= 8 u + 4 u
= 12 u

Total beads in March : Total beads in April
22 : 12 _(÷2)
11 : 6 

Answer(s): (a) 9 : 4; (b) 11 : 6